Calculate the quotient below and give your answer in scientific notation. ${\dfrac{3.8\times 10^{9}}{400}} =\ ?$
Answer: First, let's change the number in the denominator into scientific notation. ${\dfrac{3.80\times 10^{9}}{400}} = {\dfrac{3.80\times 10^{9}}{4.0\times 10^{2}}} $ Start by collecting the significands and exponents. $ {\dfrac {{3.80} \times {10^{9}}} {{4.0} \times {10^{2}}} = {\dfrac{3.80}{4.0}} \times {\dfrac{10^{9}}{10^{2}}}} $ Then divide each term separately. When dividing exponents with the same base, subtract their powers. $= {0.95} \times {10^{9 \,-\, 2}}$ $= {0.95} \times {10^{7}}$ To write the answer correctly in scientific notation, the first number needs to be between $1$ and $10$. In this case, we need to move the decimal one position to the right without changing the value of our answer. We can use the fact that ${0.95}$ is the same as ${9.5 \div 10}$, or ${9.5 \times 10^{-1}}$. $ = {9.5 \times 10^{-1}} \times {10^{7}} $ $ = 9.5 \times 10^{{-1} + {7}} $ $= 9.5\times 10^{6}$